The priest must not become unclean because of a dead body, however there are exceptions for immediate family members. The priest must remain pure by not marrying a woman that is profane. And finally anyone with a physical deformity, and a long list of those is given, shall not serve in the sanctuary. Leviticus is written for the priests and so once again these restrictions are for the priests that serve before God and do apply to everyone.

Leviticus 21

The LORD said to Moses “Speak to the priests, the sons of Aaron, and say to them ‘None of you shall become unclean for the dead. 

2 For immediate family, that is for his mother, his father, his son, his daughter, his brother;

3 If his sister is a virgin, and is close to him and she has no husband; for her may he be unclean.

4 But he must not make himself unclean for those related to him by marriage, to profane himself.

5 Priests shall not shave their heads, shave off the corners of their beards, nor make any cuttings in their flesh.

6 They shall be holy to their God, and not profane the name of their God: for the offerings of the LORD made by fire, and for the bread they offer: therefore they shall be holy.

7 They shall not take a wife that is defiled by prostitution, nor shall they take a woman divorced from her husband: for he is holy to his God.

8 You shall sanctify him, for he offers the bread of your God: he shall be holy to you: for I the LORD, who sanctifies you, am holy.

9 If the daughter of any priest profanes herself by playing the whore, she profanes her father: she shall be burned with fire.

10 And he that is the high priest among his brethren, on whose head the anointing oil was poured, that is consecrated to put on the garments, shall not uncover his head nor tear his clothes;

11 Neither shall he go near any dead body, nor defile himself for his father, or for his mother;

12 Neither shall he go out of the sanctuary, nor profane the sanctuary of his God; for the crown of the anointing oil of his God is upon him: I am the LORD.

13 He shall take a wife in her virginity.

14 He shall not marry a widow, or a divorced woman, or a woman that has been a prositute: but he shall take a virgin of his own people as his wife.

15 He shall not corrupt his bloodline among his people: for I the LORD sanctify him.’”

16 The LORD spoke to Moses, saying:

17 “Speak to Aaron and say ‘Any of your offspring in their generations that has any blemish, let him not come near to offer the bread of his God.

18 For any man that hath a blemish shall not approach: a man that is blind, lame or has a flat nose, or is disfigured; 

19 Or a man that has a broken foot or a broken hand,

20 Or a hunchback, or dwarf, or has a blemish in his eye, or has an itching disease, or scabs, or has crushed testicles.

21 No man that has a blemish of the descendants of Aaron the priest shall come near to make the offerings of the LORD by fire: he has a blemish; he shall not come near to offer the bread of his God.

22 He shall eat the bread of his God, both of the most holy, and of the holy.

23 Only he shall not go into the veil, nor come near to the altar, because he has a blemish; so that he does not profane my sanctuaries: for I the LORD do sanctify them.’”

24 And Moses told these things to Aaron, and to his sons, and to all the children of Israel.

See also: Leviticus 21 in ESV, HCSB, NASB, and NIV via Bible Gateway.